St...st...st..stuttering
Diagnosing problems at a distance is difficult, but this may help you.
The plug caps and leads may be breaking down, as your bike is an 1100 but only on low miles this might not be the problem but you must eliminate things in a logical sequence. Make sure that the ignition circuit wiring is not damaged by visual inspection, check coil mountings and earthing points for same.
You could be experiencing a throttle potentiometer mal-function or injector related fault (I'm sorry but all of these so far could produce the running fault that you describe...I'm not trying to baffle you with science.. just being helpful) Water in the fuel would tend to produce the same effect as running out of fuel and then the engine picking up again, obviouslyany water in the fuel system will be detrimental to the injectors and pump etc.
At the end of the day it might be quicker but not as cheap to go to a good bike shop and get them to investigate what the fault is, you do not have to let them repair it if you think you'r capable of making the repair. BMW dealers will probably be quicker at the diagnosis but charge more unless you visit a really good bike mechanic!
You should also make sure that the tank venting system is not blocked or resticted. If you run the engine in the dark, country lane type darkness, you may be able to see any potential ignition shorts to the HT leads and caps; if you have a garage or bike shed do this test with care and plenty of ventilation. Good luck, hope this helps you to solve the problem.